Dense clusters in hypergraphs
Combinatorics
2023-05-09 v2
Abstract
In this paper we solve the problem of finding in a given weighted hypergraph a subhypergraph with a maximum possible density. We introduce the notion of a support matrix and prove that the density of an optimal subhypergraph is equal to for an optimal support matrix . Alternatively, the maximum density of a subhypergraph is equal to the solution of a minimax problem for column sums of support matrices. We introduce the spectral decomposition of a hypergraph and show that it is a significant refinement of the Dulmage-Mendelsohn decomposition. Our theoretical results yield an efficient algorithm for finding the maximum density subhypergraph and more generally, the spectral decomposition for a given weighted hypergraph.
Cite
@article{arxiv.2304.02752,
title = {Dense clusters in hypergraphs},
author = {Yuly Billig},
journal= {arXiv preprint arXiv:2304.02752},
year = {2023}
}